Systems and methods for nonlinear distortion discovery in active carriers

ABSTRACT

A digital transmission system includes a transmitter configured to transmit an orthogonal frequency division multiplexing (OFDM) signal along a signal path, a receiver for receiving the OFDM signal from the transmitter and extracting OFDM symbols from the received OFDM signal, and a diagnostic unit configured to (i) demodulate the received OFDM signal to create an ideal signal, (ii) compare the received OFDM signal with the ideal signal to calculate an error signal, (iii) cross-correlate the error signal with the ideal signal, and (iv) determine a level nonlinear distortion from one of the transmitter and the signal path based on the correlation of the error signal with the ideal signal.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.16/249,734, filed Jan. 16, 2019, which application is a continuation ofU.S. application Ser. No. 15/711,168, filed Sep. 21, 2017, which priorapplication claims the benefit of and priority to U.S. ProvisionalPatent Application Ser. No. 62/397,772, filed Sep. 21, 2016, thedisclosures of all of which are herein incorporated by reference intheir entireties.

BACKGROUND

The field of the disclosure relates generally to digital transmissionsystems, and more particularly, to wired, wireless, and optical digitaltransmission systems employing active carriers and amplification.

Conventional OFDM transmission technology has a high crest factor, whichis the ratio of peak-to-average radio frequency (RF) power. Data OverCable Service Interface Specification (DOCSIS) technology utilizes OFDM,and experiences a crest factor of approximately 16 decibels (dB). Inpresent usage, cable operators implement one or more carriers of DOCSIS,or DOCSIS version 3.1, at high ends of the downstream cable bandwidth,and operate present coaxial amplifiers with a steep up-tilt, e.g.,approximately 15 dB. DOCSIS 3.1 signals may be as wide as 190 megahertz(MHz), and wider bandwidth typically signify greater RF power. Thus, inthis example, a DOCSIS 3.1 OFDM signal is considered to be of high RFpower, which will particularly stress the dynamic range of an amplifierat the time a transported OFDM signal crests. Moreover, as an amplifierages, its performance with respect to nonlinear distortion maydeteriorate. This problem may be further compounded by the fact thatnonlinear distortion in digital signals resembles, on conventional testequipment, like random noise, and is thus difficult to discern fromother signal impairments, such as the random noise itself, or otherinterference.

Common path distortion (CPD) is one example of nonlinear distorter on acable plant. CPD may be created, for example, by corrosion diodes, andif made by digital carriers, also resembles random noise on testequipment. CPD affects both upstream and downstream signals, and thusthere is a need to be able to find and repair CPD problems, as well as aneed to be able to find and repair distorting amplifiers that are out ofbalance, defective, or being improperly operated. In many instances, CPDoccurs from connectors, which may or may not be associated withamplifiers. Accordingly, there is also a need to determine, whereamplifiers are cascaded, which particular element(s) (e.g., which ofseveral amplifiers) of the cascade are the source of the distortion.

Upstream DOCSIS 3.1 implementations, for example, in a cable modemtransmitter, utilize orthogonal frequency division multiple access(OFDMA) modulation. Conventional cable plants may include hundreds ofsuch transmitters operating in burst mode, making it difficult to detectand locate a defective cable modem transmitter on that node. In oneexample, where a single cable modem is utilizing a maximum bandwidth of42 MHz, the single cable modem is prone to clip the upstream laser (orA-D converter) when its OFDMA signal crests.

Downstream DOCSIS 3.0 signals, on the other hand, may have a bandwidthof 6 MHz, and utilize quadrature amplitude modulation (QAM) schemes suchas 64 QAM or 256 QAM. At such relatively narrower bandwidths, suchmodulation schemes exhibit lower RF power relative to the total powerbeing amplified, and similarly have a lower crest factor relative to theOFDM signals. One conventional diagnostic technique for downstreamsignals is a “truck-roll,” which measures nonlinear distortion withequipment which physically moves along the signal path, and measuresdistortion on the signals. Diagnostic techniques presently exist, buttypically require that an in-service carrier be taken out of service sothat a test signal may be transmitted along the signal path. Exemplarysystems and methods for measuring nonlinear distortion in the vacantband are described in greater detail in U.S. Pat. Nos. 9,209,863,9,225,387, and 9,590,696, the disclosures of which are incorporated byreference herein.

Additionally, conventional diagnostic techniques for nonlineardistortion in downstream OFDM signals do not tend to produce significantor meaningful results. For example, where a 6 MHz channel is transmittedas just one of as many as 150 other channels, diagnostic test results ofthe one 6 MHz channel will not stand out significantly from the otherchannels. That is, where a square constellation is produced in the timedomain, the test results from a saturated amplifier may simply appear asmerely corners of the square constellation being pushed inward towardsthe origin. Thus, when measuring a single carrier out of 150 carriers,the corners of the resulting constellation would not exhibit significantcompression, since the distortion from other uncorrelated carriers woulddominate. In contrast, in the case of single carrier transmissions(e.g., wireless), corner compression would be more apparent.Accordingly, it is further desirable to be able to remotely performnonlinear distortion diagnostic testing without interrupting service onan in-service carrier.

BRIEF SUMMARY

In an embodiment, a digital transmission system includes a transmitterconfigured to transmit an orthogonal frequency division multiplexing(OFDM) signal along a signal path, a receiver for receiving the OFDMsignal from the transmitter and extracting OFDM symbols from thereceived OFDM signal, and a diagnostic unit configured to (i) demodulatethe received OFDM signal to create an ideal signal, (ii) compare thereceived OFDM signal with the ideal signal to calculate an error signal,(iii) cross-correlate the error signal with the ideal signal, and (iv)determine a level nonlinear distortion from one of the transmitter andthe signal path based on the correlation of the error signal with theideal signal.

In an embodiment, a method of determining a presence of nonlineardistortion in an amplified transmitted signal is provided. The methodincludes steps of capturing at least one frame of the transmitted signaland extracting symbols therefrom, demodulating the captured signal tocreate an ideal signal, calculating an error vector for each of theextracted transmission symbols, cross-correlating the created idealsignal with an error vector sequence of the calculated error vectors,and determining the presence of nonlinear distortion in the transmittedsignal according to at least one peak value resulting from the step ofcross-correlating.

In an embodiment, a method of determining a presence of nonlineardistortion in a transmitted orthogonal frequency division multiplexing(OFDM) signal is provided. The method includes steps of importing atleast one distorted OFDM block in the frequency domain, equalizing theimported OFDM frequency domain block to remove linear distortion,determining a plurality of OFDM frequency domain symbols from theequalized OFDM frequency domain block, creating a frequency domain errorseries from each of the determined OFDM frequency domain symbols,converting the equalized OFDM frequency domain block in the determinedOFDM frequency domain symbols into the time domain to form a time domaintransmission series, converting the frequency domain error series intothe time domain to form a time domain error series, cross-correlatingthe time domain transmission series with the time domain error series,and measuring a DC term for nonlinear distortion from a result of thestep of cross-correlating.

In an embodiment, a method of determining a presence of nonlineardistortion in a time domain signal is provided. The method includessteps of importing from the time domain signal, at least one distortedsignal block including a plurality of time domain symbols, equalizingthe imported time domain block to remove linear distortion, determiningthe plurality of time domain symbols from the equalized time domainblock, creating a time domain transmission series from the equalizedtime domain block and the determined plurality of time domain symbols,creating a time domain error series from each of the determinedplurality of time domain symbols, cross-correlating the time domaintransmission series with the time domain error series, and measuring aDC term for nonlinear distortion from a result of the step ofcross-correlating.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the presentdisclosure will become better understood when the following detaileddescription is read with reference to the following accompanyingdrawings, in which like characters represent like parts throughout thedrawings.

FIG. 1 is a schematic illustration depicting an exemplary digitaltransmission system, according to an embodiment.

FIG. 2 is a graphical illustration of the time domain response of areceived digital signal, in accordance with the example depicted in FIG.1.

FIG. 3 is a graphical illustration of the complex channel responsedetermined from the received digital signal depicted in FIG. 2.

FIG. 4 is a graphical illustration of a constellation plot of thereceived OFDM symbols in the frequency domain after correction of thechannel response depicted in FIG. 3.

FIG. 5 is a graphical illustration of a time domain plot of an idealtransmitted signal in relation to an error signal, in accordance with anembodiment.

FIG. 6 is a graphical illustration of a cross-correlation plot of thetransmitted signal with the error signal depicted in FIG. 5.

FIG. 7 is a graphical illustration of an overlay plot of the respectivetime domain responses of a transmitted signal and corresponding receivedsignal, according to an exemplary embodiment exhibiting moderatedistortion.

FIG. 8 is a graphical illustration of an overlay plot of the respectivetime domain responses of a transmitted signal and corresponding receivedsignal, according to an alternative embodiment exhibiting significantdistortion.

FIG. 9 is a graphical illustration of a correlation plot of the clipvoltage versus the DC term of an OFDM waveform, in accordance with anembodiment.

FIG. 10 is a flow chart diagram of an exemplary cross-correlationprocess for an OFDM signal, in accordance with an embodiment.

FIG. 11 is a graphical illustration of a plot of the input voltageversus the output voltage of an amplifier, in accordance with anembodiment.

FIG. 12 is a graphical illustration of a cross-correlation plot of thesample voltage with the average percentage error in received voltagesamples, according to an alternative embodiment.

FIG. 13 is a flow chart diagram of an alternative cross-correlationprocess for a time domain QAM signal, in accordance with an embodiment.

Unless otherwise indicated, the drawings provided herein are meant toillustrate features of embodiments of this disclosure. These featuresare believed to be applicable in a wide variety of systems including oneor more embodiments of this disclosure. As such, the drawings are notmeant to include all conventional features known by those of ordinaryskill in the art to be required for the practice of the embodimentsdisclosed herein.

DETAILED DESCRIPTION

In the following specification and the claims, reference will be made toa number of terms, which shall be defined to have the followingmeanings.

The singular forms “a,” “an,” and “the” include plural references unlessthe context clearly dictates otherwise.

“Optional” or “optionally” means that the subsequently described eventor circumstance may or may not occur, and that the description includesinstances where the event occurs and instances where it does not.

Approximating language, as used herein throughout the specification andclaims, may be applied to modify any quantitative representation thatcould permissibly vary without resulting in a change in the basicfunction to which it is related. Accordingly, a value modified by a termor terms, such as “about,” “approximately,” and “substantially,” are notto be limited to the precise value specified. In at least someinstances, the approximating language may correspond to the precision ofan instrument for measuring the value. Here and throughout thespecification and claims, range limitations may be combined and/orinterchanged; such ranges are identified and include all the sub-rangescontained therein unless context or language indicates otherwise.

As used herein, the terms “processor” and “computer” and related terms,e.g., “processing device”, “computing device”, and “controller” are notlimited to just those integrated circuits referred to in the art as acomputer, but broadly refers to a microcontroller, a microcomputer, aprogrammable logic controller (PLC), an application specific integratedcircuit (ASIC), and other programmable circuits, and these terms areused interchangeably herein. In the embodiments described herein, memorymay include, but is not limited to, a computer-readable medium, such asa random-access memory (RAM), and a computer-readable non-volatilemedium, such as flash memory. Alternatively, a floppy disk, a compactdisc-read only memory (CD-ROM), a magneto-optical disk (MOD), and/or adigital versatile disc (DVD) may also be used. Also, in the embodimentsdescribed herein, additional input channels may be, but are not limitedto, computer peripherals associated with an operator interface such as amouse and a keyboard. Alternatively, other computer peripherals may alsobe used that may include, for example, but not be limited to, a scanner.Furthermore, in the exemplary embodiment, additional output channels mayinclude, but not be limited to, an operator interface monitor.

Further, as used herein, the terms “software” and “firmware” areinterchangeable, and include any computer program storage in memory forexecution by personal computers, workstations, clients, and servers.

As used herein, the term “non-transitory computer-readable media” isintended to be representative of any tangible computer-based deviceimplemented in any method or technology for short-term and long-termstorage of information, such as, computer-readable instructions, datastructures, program modules and sub-modules, or other data in anydevice. Therefore, the methods described herein may be encoded asexecutable instructions embodied in a tangible, non-transitory, computerreadable medium, including, without limitation, a storage device and amemory device. Such instructions, when executed by a processor, causethe processor to perform at least a portion of the methods describedherein. Moreover, as used herein, the term “non-transitorycomputer-readable media” includes all tangible, computer-readable media,including, without limitation, non-transitory computer storage devices,including, without limitation, volatile and nonvolatile media, andremovable and non-removable media such as a firmware, physical andvirtual storage, CD-ROMs, DVDs, and any other digital source such as anetwork or the Internet, as well as yet to be developed digital means,with the sole exception being a transitory, propagating signal.

Furthermore, as used herein, the term “real-time” refers to at least oneof the time of occurrence of the associated events, the time ofmeasurement and collection of predetermined data, the time for acomputing device (e.g., a processor) to process the data, and the timeof a system response to the events and the environment. In theembodiments described herein, these activities and events occursubstantially instantaneously.

In an exemplary embodiment, systems and methods are provided to detectand locate nonlinear distortion in upstream and downstream OFDM andOFDMA signals, on both wired and wireless channels. In some embodiments,defects and defective devices that cause nonlinear distortion aredetected and located. In an additional or alternative embodiments,distorting amplifiers are detected and located, whether used singly, orin a cascade of multiple amplifiers. The present systems and methods maybe implemented from locations remote to the source(s) of nonlineardistortion, and will be implemented on in-service transmission lines orwireless signal paths without having to take the in-service line/pathout of service.

In an exemplary embodiment, the present systems and methods demodulatereceived signals to create ideal signals, and cross-correlate the idealsignal, or the received signals that are not made ideal, with an errorsignal to create an error vector signal. In some embodiments, a sequenceof the error vector is cross-correlated with the ideal signal, andnonlinear distortion levels are determined from the correlation peak. Inat least one embodiment, the ideal signal is created by converting anOFDM frequency domain signal into the time domain, e.g., by an inversefast Fourier transform (IFFT).

In other embodiments, samples of the ideal signal are plotted againstthe received signal, and a transfer function for distortion is derivedtherefrom, e.g., utilizing a Taylor series. The present systems andmethods maybe implemented anywhere within the network of thetransmission system, and are of particular use where the signal beingdemodulated makes up a significant portion of the total distortingpower.

FIG. 1 is a schematic illustration depicting an exemplary digitaltransmission system 100. System 100 includes a transmitter 102, anoptional amplifier 104, and a downstream receiver 106. Transmitter 102may represent, for example, a cable operator, a central office, acommunications hub, an optical hub, or an optical line terminal (OLT),and may include additional receiver circuitry (not shown), or may be atransceiver capable of both transmission and reception. Where present,amplifier 104 may be, for example, a single amplification source, or acascade of multiple amplifiers disposed along a downstream transmissionpath of system 100. In some embodiments, transmitter 102 is a broadcasttransmitter that creates distortion in the broadcast, and system 100does not include amplifier 104 between transmitter 102 and receiver 106.Downstream receiver 106 may be, for example, a downstream terminationunit, which may include, without limitation, a customer device (e.g., amobile telephone, a cable modem, a cable modem termination system(CMTS), etc.), customer premises (e.g., an apartment building), abusiness user, or an optical network unit (ONU).

In exemplary operation, transmitter 102 transmits an OFDM signal 108 inthe downstream direction D to amplifier 104 over a first downstreamtransmission line 110. Amplifier 104 amplifies OFDM signal 108, andrelays and amplified OFDM signal 112 in the downstream direction D todownstream receiver 106 over a second downstream transmission line 114.In the embodiments described further below, amplified OFDM signal 112includes nonlinear distortion from amplifier 104, and/or other nonlinearinterference sources along the downstream transmission path of system100. In some embodiments, receiver 106 represents a plurality ofseparate receivers 106 (not separately illustrated).

In an alternative or supplemental operation, downstream receiver 106includes an upstream transmission unit 116, capable of transmitting anOFDMA signal 118 in the upstream direction U to amplifier 104 along afirst upstream transmission line 120. Amplifier 104 then relays andamplified OFDMA signal 122 in the upstream direction U to transmitter102 along a second upstream transmission line 124. Downstream receiver106 and upstream transmission unit 116 may be separate devices, or mayconstitute a single transceiver device. In some embodiments, upstreamtransmission unit 116 represents a plurality of separate upstreamtransmission units 116 (not separately illustrated), and amplifier 104may further include a multiplexer or combiner (not shown) to combinemultiple respective OFDMA signals 118 into a single amplified OFDMAsignal 122.

Upstream transmission lines 120, 124 may be separate from downstreamtransmission lines 110, 114, or the upstream and downstreamtransmissions may be shared along a single transmission line capable oftransmitting multiple signals in both the upstream and downstreamdirections. In coaxial implementations, amplifier 104 is a two-wayamplifier, and a common coaxial cable is utilized for the upstream anddownstream transmissions. For the examples described with respect tosystem 100, transmission lines 110, 114, 120, 124 are described, forease of explanation, as tangible transmission media, such as coaxialcable, electrical wires, and/or fiber optics. The principles of thepresent systems and methods though, are also applicable to wirelesstransmission paths and/or transmission bands (e.g., Wi-Fi, LTE, LTE-U),which, as described above, may optionally exclude amplifier 104 from thesignal path.

The graphical and data results, as described with respect to theembodiments below, illustrate several examples of signal processing anddiagnostic testing that may be performed by a diagnostic unit 126, whichmay be part of transmitter 102, part of receiver 106, and/or a separateand independent unit. In some embodiments, diagnosed unit 126 may be asoftware module stored in a memory (not shown) of transmitter 102 orreceiver 106 (or a separate unit), and executed by a respectiveprocessor (also not shown) thereof.

In at least one example, the performance and functionality of diagnosticunit 126 may be produced from a test simulation of system 100. Forexample, system 100 may be simulated utilizing a LeCroy ArbitraryWaveform Generator ArbStudio 1102, controlled by a programmed PC,operating as transmitter 102, and a LeCroy HDO-6104 digital oscilloscopeoperating as receiver 106. In operation of the simulation, the ArbitraryWaveform Generator generates an OFDM signal (occupying the 5-85 MHzrange in this example) and creates distortion in the amplifier. Theresulting distorted waveform is captured by the digital oscilloscope. Inthe simulation, increases in the signal level, as well as increases ordecreases in the simulated nonlinear distortion, may be adjusted by pad(attenuator) changes. This test configuration thus approximatelysimulates a cable OFDM and OFDMA transmission system, and verifies theseveral plots and/or correlations described below.

FIG. 2 is a graphical illustration of a time domain response 200 of adigital signal 202 received in system 100, FIG. 1. In the exemplaryembodiment, digital signal 202 is an OFDM signal including a first burstportion 204 and a second burst portion 206. In some embodiments, firstburst portion 204 is a quadrature phase shift keying (QPSK) test signalutilized for channel characterization, and second burst portion 206 is ahigher-amplitude signal with respect to first burst portion 204, and maybe a 64 QAM OFDM signal that includes nonlinear distortion.

In operation, a downstream OFDM frame of digital signal 202 is capturedat a terminal device (e.g., receiver 106, FIG. 1). In some embodiments,simple network management protocol (SNMP) management information bases(MIBs) are utilized in a DOCSIS implementation, and frame capture mayalternatively be performed using a vector signal analyzer. In at leastone embodiment, frame capture is performed using a baseband capturedevice, such as a digital oscilloscope, and an FFT may be executed onthe signal captured thereby. In the example illustrated in FIG. 2,response 200 represents a captured time series waveform from a digitaloscilloscope, and plotted as frequency domain I-Q symbols that have beentransformed into the time domain, for a sample rate of 250 millionsamples per second. First burst portion 204 thus includes Q PSK trainingsymbols, and second burst portion 206 includes 64 QAM symbols. Secondburst portion 206 thus simulates, and/or functionally represents, a 5-85MHz DOCSIS 3.1 OFDMA transmission.

FIG. 3 is a graphical illustration of a complex channel response 300determined from first burst portion 204, FIG. 2. Response 300 includes alinear magnitude component 302, and a phase component 304. In anexemplary functional operation, response 300 may be obtained byperforming a frequency domain characterization of the respective channelfrom which response 300 is received, effectively using signal 204 as atraining signal or channel characterization signal. The obtained channelresponse may then be used to perform equalization.

FIG. 4 is a graphical illustration of a constellation plot 400 ofreceived OFDM symbols 402 in the frequency domain after correction usingchannel response 300, FIG. 3. In an exemplary embodiment, the pointspread of OFDM symbols 402 may be caused by nonlinear distortion, noise,or both. In an exemplary operation, OFDM frequency domain symbols 402are sliced to create a “perfect” noise- and distortion-freeconstellation. Thus, in constellation 400, the 64 constellation pointsall become represented as dots. In further operation, a frequency domainerror vector may be created for each of OFDM symbols 402. The errorvectors may be computed as the Euclidian distance from the ideallocation of a particular symbol to the actual measured location of thedistorted/noisy symbol. In this example, it is presumed that no slicingerrors occur, and that all symbols are within respective correctdecision thresholds.

FIG. 5 is a graphical illustration of a time domain plot 500 of an idealtransmitted signal 502 in relation to an error signal 504. In theexample illustrated in FIG. 5, the time series of error signal 504 isrepresented by the black line, and the time series of ideal transmittedsignal 502 is represented by the grayscale line. In exemplary operation,ideal transmitted signal 502 is obtained by converting noise-freefrequency domain symbols 402, FIG. 4, into the time domain using anIFFT, which effectively results in the unimpaired complex time seriesthat is ideal transmitted signal 502. In an exemplary DOCSISimplementation, FFT/IFFT size may be 2048, 4096, or 8192 complex symbols(e.g., signal 502). Similarly, error signal 504 is obtained byconverting the error vectors (described above with respect toconstellation 400, FIG. 4) into a time domain series (e.g., also usingan IFFT).

Response 500 thus demonstrates several particular relationships that mayexist with respect to OFDM transmissions regarding distortion, andresulting error signals. For example, it can be seen from FIG. 5 that,at times when the time domain ideal transmitted signal 502 crests in thenegative direction, the corresponding error signal 504 increases in thepositive direction. It may also be noted from FIG. 5 that, for theamplifier utilized in this example, distortion is more prevalent whenideal submitted signal 502 moves in the negative direction, as opposedto movement in the positive direction.

FIG. 6 is a graphical illustration of a cross-correlation plot 600 ofideal transmitted signal series 502 with error signal series 504, FIG.5. Plot 600 includes DC term 602 and adjacent term 604, which are causedby nonlinear distortion. Portions of plot 600, between DC term 602 andadjacent term 604, result from the convolution of error signal 504, FIG.5, with the non-cresting OFDM signal samples, random noise, as well asother ingressing signals. As can be seen from FIG. 6, the DC termsincrease rapidly with an increase in distortion levels.

In exemplary operation plot 600 is obtained by cross-correlating theunimpaired time domain series 502 with the time domain error vectorssignal 504. If nonlinear distortion is present, there will be aresulting DC term in the correlation results of plot 600, or evenadjacent terms (peaks) on both ends, as illustrated in FIG. 6, with DCpeak located at one end. The DC term is caused by a temporal peak notbeing achieved at the terminal unit due to clipping or othersignal-limiting phenomena. The amplitude of the DC term indicates thelevel of nonlinear distortion in the signal. Otherwise, the result ofthe convolution resembles random noise, because at the instant atransmitted signal peaks in power, a time domain error is created.Mathematically, it may be noted that multiplication in the frequencydomain may often be used as a functional equivalent to convolutions inthe time domain. Thus, in an alternative embodiment, frequency domainprocessing may be used instead of the time domain convolution function.Mathematically, signal clipping may perform the same function assubtracting the clipped (or missing) voltage from an original signal.

FIG. 7 is a graphical illustration of an overlay plot 700 of respectivetime domain responses of a received signal 702 (illustrated ingrayscale) overlaid on a corresponding transmitted signal 704(illustrated in black), in the presence of moderate distortion/clippinglevels. Received signal 702 represents values of transmitted signal 704,minus the error, as described above. Thus, in an overlay plot, receivedsignal 702 would completely cover transmitted signal 704 where no errorsignal was present. In contrast, where the error signal is present,clipping occurs, and portions of transmitted signal 704 are visiblebehind corresponding portions of received signal 702 (i.e., whereclipping occurs). It can be further noted from the illustration of FIG.7 that more clipping occurs (i.e., more of transmitted signal 704 isvisible) where signals 702, 704 move in the negative direction, asopposed to less visible clipping in the positive direction.

FIG. 8 is a graphical illustration of an overlay plot 800 of respectivetime domain responses of a received signal 802 data for (illustrated ingrayscale) overlaid on a corresponding transmitted signal 804(illustrated in black), in the presence of significant (e.g., severe)distortion/clipping levels. Similar to overlay plot 700, FIG. 7, above,received signal 802 represents values of transmitted signal 804, minusthe error. Thus, where the more significant error signal is present,greater levels of clipping occur, and much larger portions oftransmitted signal 804 are visible behind corresponding portions ofreceived signal 802.

According to embodiments described above (and also further below), ifslicing errors occur, the slicing errors may be determined utilizingforward error correction (FEC), and a successful FEC solution may comeup in an alternative embodiment, be solved in reverse to determine whatwas ideally transmitted. That is, a corrected time series may bedetermined through the FEC implementation, instead of the use of theIFFT, described above. In at least some embodiments, where simultaneoussymbol capture is performed at the headend (e.g., at transmitter 102,FIG. 1) and/or in the field, the headend OFDM signal would be expectedto be error-free, and therefore may be used to create an ideal transmitsignal. With respect to upstream transmission, a triggered CMTS spectrumanalysis may be implemented to evaluate the transmission of eachrespective cable modem. This alternative subprocessing is of particularvalue where cable modems are operating at or near maximum power, andwould thus be expected to produce more nonlinear distortion than cablemodems operating at lower power levels. Such processing techniques mayalso reveal nonlinear distortion originating inside a home environment,such as from a corrosion diode, or an overloaded passive component suchas a splitter.

FIG. 9 is a graphical illustration of a correlation plot 900 of a clipvoltage 902 versus a DC term 904 of an OFDM waveform (not shown in FIG.9), according to the embodiments described above. In the exampleillustrated in FIG. 9, the OFDM waveform is clipped for both positiveand negative voltages. Accordingly, as the severity of the clippingincreases, distortion rises rapidly. That is, correlation plot 900demonstrates how nonlinear distortion levels (i.e., DC term 904)increase rapidly as the clipping severity increases. In someembodiments, correlation plot 900 may be produced mathematically, byutilizing both the high- and low-clipping portions of a received OFDMsignal (e.g., digital signal 202, FIG. 2). In the exemplary embodiment,the principles described herein are further advantageous value for othertypes of OFDM transmission systems, including without limitation,broadcast (e.g., ATSC-3, DVB-T etc.) and OFDM transmissions from LTEcell towers.

FIG. 10 is a flow chart diagram of an exemplary cross-correlationprocess 1000 for an OFDM signal, in accordance with embodimentsdescribed above. Process 1000 begins at step 1002, in which a distortedOFDM block or frame (e.g., frame of digital signal 202, FIG. 2),including a plurality of OFDM symbols, is imported as a frequency domainsignal, or alternatively converted into the frequency domain. In step1004, the imported/converted frequency domain block is equalized toremove linear distortion. (See e.g., FIG. 3). In step 1006, the correctOFDM symbols are determined from the equalized frequency domain block.(See e.g., FIG. 4). In step 1008, a frequency domain error series iscreated for each of the frequency domain OFDM symbols determined in step1006. (See e.g., FIG. 4). In step 1010, a time domain transmissionseries is created (e.g., by an IFFT) from the equalized frequency domainblock and OFDM symbols resulting from steps 1004 and 1006. (See e.g.,FIG. 5). In step 1012, a time domain error series is created (e.g., alsoby an IFFT) from the frequency domain error series created in step 1008.(See e.g., FIG. 5). In step 1014, the ideal time domain transmissionseries created in step 1010 is cross-correlated with the time domainerror series created in step 1012. (See e.g., FIG. 6). In step 1016, theDC term for nonlinear distortion is measured. (See e.g., DC term 904,FIG. 9).

FIG. 11 is a graphical illustration of a plot 1100 of an input voltage1102 versus an output voltage 1104 of an amplifier (e.g., amplifier 104,FIG. 1). In the exemplary embodiment, plot 1100 represents a curve thatmay be smoothed by averaging, and then analyzed for Taylor seriescoefficients. In at least one embodiment, the Taylor series is obtainedby first plotting ideal symbol values against actual received symbolsamples, which will result in a series of plot points 1102 thatcollectively produce a bending line shape for plot 1100, from whichcurve fitting techniques may be applied to derive the Taylor seriescoefficients. In this example, the bending line shape of plot 1100 isillustrative of a transfer function, and fewer points appear at thehighest and lowest voltage levels due to the Gaussian distribution ofthe OFDM test signal used to produce the data results for FIG. 11.

In some embodiments, the OFDM signal may be captured as a complexsignal, or with a non-DC center frequency. In such instances, thecaptured OFDM signal may be first converted into a baseband (i.e., DC)signal before analysis and Taylor series derivation. That is, the signalanalysis and derivation processes are performed on the converted realsignal, and not on the captured complex signal. In some embodiments,these techniques are of particular value with respect todistortion-producing elements, such as laser diodes, which may clipunsymmetrically.

As described above, the advantageous embodiments herein are useful for avariety of OFDM signals that contain nonlinear distortion. Systems andmethods according to these embodiments are capable of realizingsignificant advantages over conventional transmission systems. Forexample, implementing the present embodiments, a modulation error ratio(MER) for one or more of the several system components may be decomposedaccording to whether distortion may be nonlinear, random, and/orperiodic (such as with a continuous wave (CW) ingress or signal).Additionally, diagnostic testing according to the present embodimentsmay be repeated in a sequence down a cascade of multiple amplifiers, inorder to identify and locate a defective amplifier in the cascade. Insome embodiments, where the diagnostic testing is performed remotely,each amplifier in the cascade may be diagnosed with substantialsimultaneity. In at least one alternative embodiment, innerconstellation points (see e.g., FIG. 4) may be utilized and set of pilotsignals, in order to establish the presence of non-distorted symbols,and then to accurately establish slicing thresholds.

In an example of a DOCSIS 3.1 implementation, the present systems andmethods may be executed with simultaneous symbol capture (e.g.,unimpaired OFDM symbol capture at the headend). In such implementations,there should be no slicing errors, should have no slicing errors, andthe captured symbols may be used to create an unimpaired signal forconvolution with an error signal, which may also be captured from thefield from multiple locations simultaneously.

In an alternative implementation, two or more OFDM blocks aresimultaneously captured, recorded, and combined, such that the combinedOFDM block may be processed as a single higher-power and wider-bandwidthsignal when performing the digital signal processing. For time domaintransmissions in particular, such OFDM block combination techniques areadvantageous for multiple 6 MHz 256QAM single carrier signals, forexample, many of which may be combined into a single block and processedas a single wideband signal. In some instances, when multiple signalsare combined, the Central Limit Theorem may apply, and the resultingcomposite signal may become more Gaussian in its plotted appearance.

In further alternative embodiments, different processing steps may besubstituted for the cross-correlation subprocesses. Such alternativesubprocesses are also capable of determining if, at times when themagnitude of a transmitted signal crests, the error signal also crests(i.e., a corresponding received signal is unable to reach the samemagnitude level as the transmitted signal). Examples of such alternativeembodiments are described further below with respect to FIGS. 12-13.

FIG. 12 is a graphical illustration of a cross-correlation plot 1200 ofa sample voltage 1202 with an average percentage error 1204 in thereceived voltage samples. As illustrated in FIG. 12, individual timedomain signal samples are collected and arranged into “bins” accordingto magnitude. Because an OFDM signal is expected to peak onlyoccasionally, significantly more signal samples will be grouped into thelower-power bins then into the higher-power bins. Once the signalsamples are so grouped, an average error ratio for each been may becomputed, and the results thereof then plotted as plot 1200.

As illustrated in FIG. 12, because of the relatively smaller number ofsamples contained within the higher-power bins, the higher-power binswill experience greater levels of random error due to less averaging.That is, where the voltage is higher, so is the average error, which iscaused by nonlinear distortion. In at least one embodiment, data fromplot 1200 is arranged into a histogram (not shown) for the number ofsamples versus power, which would indicate whether the received signalis Gaussian, or non-Gaussian, shaped. In this example, plot 1200 isdrawn for illustration purposes, and should not be considered as beingdrawn to-scale. Implementations of a testing scheme according to FIG. 12are further useful for non-OFDM signals utilizing an amplifier,including without limitation, audio amplifier/speaker performance, aswell as other types of modulated signals or modulation techniques, suchas code division multiple access (CDMA) and/or wavelet modulation.

FIG. 13 is a flow chart diagram of an alternative cross-correlationprocess 1300 for a time domain QAM signal (or other types of transmittedtime domain signals, as described herein). Process 1300 is similar toprocess 1000, FIG. 10, except that the error signal determination inprocess 1300 is substantially performed in the time domain, as opposedto the frequency domain. Process 1300 begins at step 1302, in which ablock of the time domain QAM signal, including a plurality of timedomain QAM symbols, is imported. In step 1304, the imported time domainblock is equalized to remove linear distortion. In step 1306, thecorrect QAM symbols are determined from the equalized time domain block.In step 1308, time domain transmission series is created from theequalized time domain block and QAM symbols resulting from steps 1304and 1306. In step 1310, a time domain error series is created for eachof the time domain QAM symbols determined in step 1306. In step 1312,the time domain transmission series created in step 1308 iscross-correlated with the time domain error series created in step 1310.In step 1314, the DC term for nonlinear distortion is measured.Accordingly, the present systems and methods are advantageously usefulsignals transmitted and received in both the time domain and thefrequency domain.

Systems and methods according to the present embodiments representfurther significant improvements over conventional transmission schemesby providing dynamic detection and location of nonlinear distortionsources for active time domain and frequency domain carriers (i.e.,single carrier and multicarrier). Nonlinear distortion may be determinedby demodulating a received signal to create an ideal signal, determiningan error vector for each received symbol, and cross-correlating theerror vector sequence with the ideal signal to indicate the presence ofnonlinear distortion from the correlation peaks. For OFDM frequencydomain signals, frequency domain data may be converted into the timedomain before cross-correlation is performed.

The present embodiments provide further advantages over conventionalsignal processing techniques, by plotting received signal samplesagainst ideal samples and deriving a transfer function from the curveplotted therefrom. Where slicing errors are present with respect to thereceived signal, FEC solutions may be implemented in reverse to obtainthe ideal signal. The present embodiments are useful in a variety ofsignal transmissions in transmission schemes, including withoutlimitation, OFDM, OFDMA, DOCSIS, SC-FDMA, QAM, QPSK, ATSC/ATSC-3, DVB-T,LTE, and LTE-U.

Although specific features of various embodiments may be shown in somedrawings and not in others, this is for convenience only. In accordancewith the principles of the systems and methods described herein, anyfeature of a drawing may be referenced or claimed in combination withany feature of any other drawing.

Some embodiments involve the use of one or more electronic or computingdevices. Such devices typically include a processor, processing device,or controller, such as a general purpose central processing unit (CPU),a graphics processing unit (GPU), a microcontroller, a reducedinstruction set computer (RISC) processor, an application specificintegrated circuit (ASIC), a programmable logic circuit (PLC), aprogrammable logic unit (PLU), a field programmable gate array (FPGA), adigital signal processing (DSP) device, and/or any other circuit orprocessing device capable of executing the functions described herein.The methods described herein may be encoded as executable instructionsembodied in a computer readable medium, including, without limitation, astorage device and/or a memory device. Such instructions, when executedby a processing device, cause the processing device to perform at leasta portion of the methods described herein. The above examples areexemplary only, and thus are not intended to limit in any way thedefinition and/or meaning of the term processor and processing device.

This written description uses examples to disclose the embodiments,including the best mode, and also to enable any person skilled in theart to practice the embodiments, including making and using any devicesor systems and performing any incorporated methods. The patentable scopeof the disclosure is defined by the claims, and may include otherexamples that occur to those skilled in the art. Such other examples areintended to be within the scope of the claims if they have structuralelements that do not differ from the literal language of the claims, orif they include equivalent structural elements with insubstantialdifferences from the literal language of the claims.

What is claimed is:
 1. A digital communication system, comprising: areceiver for receiving a first signal over a signal path and extractingsymbols from the received first signal, the received first signal havinga first modulation format; and a diagnostic unit configured to (i)demodulate the received first signal to create an ideal signal, (ii)compare the received first signal with the ideal signal to derive atransfer function, and calculate an error signal based on the derivedtransfer function, (iii) cross-correlate the error signal with the idealsignal, and (iv) determine a level nonlinear distortion received fromthe signal path based on the correlation of the error signal with theideal signal.
 2. The system of claim 1, wherein the diagnostic unit isfurther configured to equalize linear distortion from the amplifiedfirst symbols.
 3. The system of claim 1, wherein the diagnostic unit isfurther configured to calculate the error signal by computing an errorvector for each symbol of the extracted first symbols.
 4. The system ofclaim 3, wherein the error signal is calculated by establishing an errorvector sequence from the computed error vectors of the extracted firstsymbols.
 5. The system of claim 1, wherein the level of nonlineardistortion is determined from at least one peak value of the correlationof the error signal with the ideal signal.
 6. The system of claim 1,wherein the diagnostic unit is further configured to create the idealsignal using an inverse Fourier transform.
 7. The system of claim 1,wherein the derived transfer function is a Taylor series.
 8. The systemof claim 1, wherein the diagnostic unit is further configured to createthe ideal signal by performing a reverse forward error correctionsolution on the received first signal.
 9. The system of claim 1, whereinthe receiver comprises the diagnostic unit.
 10. The system of claim 1,further comprising an amplifier for amplifying a radio frequency powerof the received first signal.
 11. The system of claim 10, wherein theamplifier comprises a plurality of amplifiers in a cascade.
 12. Thesystem of claim 11, wherein the diagnostic unit is further configured todetermine a level of nonlinear distortion for each amplifier of theplurality of amplifiers in the cascade.
 13. The system of claim 1,wherein the first modulation format comprises at least one of OFDM,OFDMA, DOCSIS, SC-FDMA, QAM, QPSK, ATSC/ATSC-3, DVB-T, LTE, and LTE-U.14. A method of determining a presence of nonlinear distortion in areceived signal, comprising the steps of: capturing at least one frameof the received signal and extracting symbols therefrom in the frequencydomain; demodulating the captured signal to create an ideal signal,further comprising a substep of performing an inverse Fourier transformon the captured signal; calculating an error vector for each of theextracted symbols; cross-correlating the created ideal signal with anerror vector sequence of the calculated error vectors; and determiningthe presence of nonlinear distortion in the received signal according toat least one peak value resulting from the step of cross-correlating.15. The method of claim 14, wherein the received signal comprises aquadrature amplitude modulation signal in the time domain.
 16. Themethod of claim 14, wherein the received signal comprises an orthogonalfrequency division multiplexing (OFDM) signal in the frequency domain.17. The method of claim 16, wherein the step of creating the idealsignal comprises performing an inverse Fourier transform on the OFDMsignal.
 18. The method of claim 16, further comprising the step ofequalizing the captured signal to remove linear distortion.
 19. Themethod of claim 14, wherein the received signal comprises at least oneof an OFDMA, DOCSIS, SC-FDMA, QAM, QPSK, ATSC/ATSC-3, DVB-T, LTE, andLTE-U signal.